Is using a quote from someone deceased since the 1940’s on a movie poster illegal?

You question raises three legal areas to investigate.  The first is the possibility of a copyright held by WC Fields' estate or the movie studio that produced the work where the quote derived.  It is likely that the quote is no longer protected under the Copyright Act, since the quote occurred prior to 1978.  The duration runs from when it was first published, not WC's death (17 U.S.C. 304).  You will need to identify the create & publish date.  Next, depending on that timeframe the copyright holder's may be required to renew the copyright in order to extend it to the full 95 year term they have available.  If they renewed then the copyright would likely still be valid and you will need license to include the quote on the movie poster.

Second, you must investigate the Trademark implications.  If the WC Fields' estate or any other business has used the quote so that consumers recognize it as identifying a company or product you may run the risk of trademark infringement or dilution.  The best example of a copyright that became a trademark is Mickey Mouse (Walt Disney is also the believed lobbiest behind the extension of the copyright term to the life of the creater plus 70 years).  You can search TESS (the trademark database at http://www.uspto.gov/) to see if anyone has a federal registration.  Although, TESS will not end your investigation as a company is not required to register in order to have a trademark.  A google search may reveal other businesses or sources that are using the quote, but you should really seek out an attorney if you need ultimate piece of mind.  In the event someone brings an infringement suit against you, the judge could grant a preliminary injunction preventing you from using your posters during the most critical marketing time.

Third, there is a possibility of violating Fields' estate's publicity rights.  State law governs these rights and the differences state-to-state are vast.  A publicity right is similar to a copyright, but gives a person control over the use of their image, voice, mannerisms, etc.  I always think of those Hoover Vacuum commercials where Fred Astaire postumously danced with a vacuum.  His estate licensed the publicity rights for the commercial whereas the movie studio owning the copyrights licensed them.  

Merely using the quote without the image or reference to the original film may absolve all concerns over any of these three.  An attorney may be able to help you design the poster so that it meets the artistic vision of your client while also avoiding any of these pitfalls.  Also, you could approach the owners of the rights, verify that they actively claim rights, and ask for a free or cheap license.